Do T asymmetries for neutrino oscillations in uniform matter have a CP-even component?

Abstract

Observables of neutrino oscillations in matter have, in general, contributions from the effective matter potential. It contaminates the CP violation asymmetry adding a fake effect that has been recently disentangled from the genuine one by their different behavior under T and CPT. Is the genuine T-odd CPT-invariant component of the CP asymmetry coincident with the T asymmetry? Contrary to CP, matter effects in uniform matter cannot induce by themselves a non-vanishing T asymmetry; however, the question of the title remained open. We demonstrate that, in the presence of genuine CP violation, there is a new non-vanishing CP-even, and so CPT-odd, component in the T asymmetry in matter, which is of odd-parity in both the phase δ of the flavor mixing and the matter parameter a. The two disentangled components, genuine AαβT;CP and fake AαβT;CPT, could be experimentally separated by the measurement of the two T asymmetries in matter (να ↔ νβ) and ( {overline{nu}}_{alpha}leftrightarrow {overline{nu}}_{beta } ). For the (νμ ↔ νβ) transitions, the energy dependence of the new AμeT;CPT component is like the matter-induced term AμeCP;CPT of the CP asymmetry which is odd under a change of the neutrino mass hierarchy. We have thus completed the physics involved in all observable asymmetries in matter by means of their disentanglement into the three independent components, genuine AαβCP;T and fake AαβCP;CPT and AαβT;CPT.